Northcott property and universality of higher degree forms

被引：0

作者：

Prakash, Om ^{[1
]}

机构：

[1] Charles Univ Prague, Fac Math & Phys, Dept Algebra, Sokolovska 83, Prague 8, Czech Republic

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2025年 / 21卷 / 03期

关键词：

Northcott property; m-ic lattices; universal higher degree forms; totally real fields; orders; QUADRATIC-FORMS; RANK; NORM;

D O I：

10.1142/S1793042125500344

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K be a totally real number field, d a positive integer, and Q a higher degree form over K. We prove that there are at most finitely many totally real extensions L/K of degree d such that Q over L is universal. Further, we show that there are no universal forms over totally real infinite extensions of & Qopf; having the Northcott property.

引用

页码：675 / 694

页数：20

共 50 条

[41] NORM PRINCIPLES FOR FORMS OF HIGHER DEGREE PERMITTING COMPOSITION
Fitzgerald, R. W.
Pumpluen, S.
COMMUNICATIONS IN ALGEBRA, 2009, 37 (11) : 3851 - 3860
[42] Skew-holomorphic Jacobi forms of higher degree
Hayashida, S
Automorphic Forms and Zeta Functions, 2006, : 130 - 139
[43] On centres and direct sum decompositions of higher degree forms
Huang, Hua-Lin
Lu, Huajun
Ye, Yu
Zhang, Chi
LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (22): : 7290 - 7306
[44] NONDEGENERATE HIGHER DEGREE FORMS OVER DEDEKIND DOMAINS
COLEMAN, DB
CUNNINGHAM, J
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 52 (OCT) : 65 - 68
[45] Generating Whitney forms of polynomial degree one and higher
Bossavit, A
IEEE TRANSACTIONS ON MAGNETICS, 2002, 38 (02) : 341 - 344
[46] On the Northcott property for special values of L-functions
Pazuki, Fabien
Pengo, Riccardo
REVISTA MATEMATICA IBEROAMERICANA, 2024, 40 (01) : 1 - 42
[47] On the Northcott property and other properties related to polynomial mappings
Checcoli, Sara
Widmer, Martin
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2013, 155 (01) : 1 - 12
[48] On the Northcott property of zeta functions over function fields
Genereux, Xavier
Lalin, Matilde
Li, Wanlin
FINITE FIELDS AND THEIR APPLICATIONS, 2022, 83
[49] Gauge-invariant theories and higher-degree forms
Salgado, S.
JOURNAL OF HIGH ENERGY PHYSICS, 2021, 2021 (10)
[50] Automorphisms of certain forms of higher degree over ordered fields
Chlebowicz, A
Sladek, A
Wolowiec-Musial, M
LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 331 (1-3) : 145 - 153

← 1 2 3 4 5 →